Rhumb line calculator or distance and course computer



KR 2 9 405 9113 QQLELAQRQH CRGSSREFERENCE Aug; 6, 1946. J. E. CLEMONS EI'AL 2,405,113

RHUMB LINE CALCULATOR on DISTANCE AND-COURSE COMPUTER Filed April 6, 1944 2 Sheets-Sheet 1 27 0 NA TICAL 2 00 (\LE 43 36 I 2 3 29 Jrwwwtow Mow;

RHUMB LINE CALCULATOR OR DISTANCE AND COURSE COMPUTER Filed April 6, 1944 2 Sheets-Sheet 2 COURSE ulin DL: Place crosvluir over DL Reva ve disc until distance is g dimly ova DL under the Read COURSE above arrow on lower sale of 45 to B9 If 0 min: the uientDI-o w ul Place mf -hair ova: quivzlm: DL Revolve disc until distance is dircfl-ly aver equivalent DI. unde: lhc crouhair. Read COURSE above arrow on upper gal: of 4S :0 0'60 clockwise.

lo 901i A DISTANCE AND COURSE COMPUTER 45 Patented Aug. 6, 1946 RHUMB LINE CALCULATOR OR DISTANCE AND COURSE COMPUTER John E. Clemons, San Antonio, and John G. Nelson, Houston, Tex.

Application April 6, 1944, Serial No. 529,808

2 Claims.

This invention relates to navigational devices for a man-made structure that may travel by air, land, or water, and has special reference to a navigational device for quickly determining the distance between points identified by latitude and longitude and also for determining the proper direction or azimuth. The proper direction in such case is the course of the rhumb-line, A rhumb-line course crosses all meridians at the same angle, while great circle courses, excepting at the equator, are always changing in reference to meridians and cross no two meridians at the same angle. A further object of the invention is to provide a device whereby the rhumb-line distance between two points on the surface of the globe that lie within the limitations of the computer may be quickly and accurately determined.

A still further object of the invention is to provide a simple device whereby the direction course or azimuth in traveling from one such point to another may be determined.

A further important object of the invention is to provide a device whereby the calculations for rhumb-line distance and course may be made without requiring reference to any tables, such as tables of trigonometric functions, or logarithms.

With the above and other objects in view as will hereinafter be apparent, the invention consists in general of certain novel details of construction, arrangement of scales, and combination of parts hereinafter fully described, as 11- lustrated in the accompanying drawings, and herein specifically claimed.

In the accompanying drawings, like characters of reference indicate like parts in the several views, and:

Figure 1 is a plan view of one side, termed the I back of the device in its-preferred embodiment.

Figure 2 is a plan view of the other side, termed the front of the device in its preferred embodiment.

Figure 3 is an edge elevation of the device.

Figure 4 is a section taken on line 4-4 of Fig. l of a transparent cursor showing a preferred construction of a slide mounted thereupon, which will be described below.

In the construction of this invention, there is provided a flat plate made of suitable material such as (but not restricted to) stiff cardboard, metal or plastic. This may be opaque. This scale twice circumscribes the inner scale, and on ,the first revolution it is marked by increasing increments from 0 to 3,000; and on the second revolution it is marked by increasing increments from 3,000 to 4,200. It is indicated at |5 by the words Rhumb-line distance-nautical miles.

On the centered pivot II, on the back side of the computer, is mounted a rotatable disc I6, the periphery of which coincides with the markings of the scale l2. This disc is marked with a series of curves running, from 0 degrees to degrees and indicated at intervals as shown by l8. This disc is marked Longitude difference (from equator to 75) by l9. It will be observed that on the disc is further marked at 20, Navigator must know in degrees and minutes: 1. Difference of latitude DL; 2. Difierence of longitude DLo; 3. Mid-latitude ML. Distance: Place arrow 41 of DLo disc over DL. Place slide of ML scale of tab at ML. Revolve tab until ML is directly over DLo. Read Distance under hair-line. Equivalent DL: Place arrow of DLo disc over zero. Place slide of ML scale of tab at ML. Revolve tab until ML is directly over DLo. Read Equivalent DL under hair-line. Pivoted to, and capable of rotation independently of the disc, on pivot on the back side of the computer, is also a transparent cursor 2|, having a center line 22 along which, by increasing and decreasing increments 23, are divisions from 0 degrees to 75 degrees. It will be noted that at 24 is marked on this cursor, Mid-latitude scale. The midlatitude figure is half the sum'of the latitudes of the two places (if both are on the same side of the equator). It will be noted at 25 there is a transparent slide with a cross-hair 26, which latter forms a right angle to acenter line 22 of the cursor 2|. The slide 25 can be moved lengthwise of the cursor 2|, toward and away from the pivot II. This slide is illustrated, in section, in Figure 4. It will be noted that on the periphery of disc Hi there is an index arrow 41.

, The other side of the plate is the front thereof and is marked Front" at 21. On this side of the plate there is mounted a disc 28 which while coaxial with pivot II is non-rotatable thereon, the disc being held against rotation by a suitable means such as the rivet 29. On the periphcry of disc 28 is a scale 30 of increasing increments from 45 degrees to 89 degrees-30 minutes, which is marked counter-clockwise. Adjacent to and inside of this scale, is a scale 3| from degrees-30 minutes to 45 degrees of decreasing increments which is marked clockwise. These angles represent course of travel. From markings 45 degrees to 0 degrees is a marking Warning at 33. On this disc at 34 are also the markings: Course using DL: Place cross-hair over DL. Revolve disc until distance is directly over DL under the cross-hair. Read Course above arrow on lower scale of 45 to 89-30 counterclockwise. If arrow points to Warning space, solve by using equivalent DL. At 35 are markings Course using equivalent DL: Determine the equivalent DL on back of rule. Place cross-hair over equivalent DL. Revolve disc until distance is directly over equivalent DL under the crosshair. Read Course above arrow on upper scale of 45 to 0-30' clockwise. Beneath this stationary disc 28 is another disc 36 rotatable on pivot H which has markings 31, from 50 to 4,000 of decreasing increments, reading clockwise. This is marked at 38 by Distance nautical miles. There is an index arrow 39 which points to the periphery of the non-rotatably secured disc 28. About the periphery of the revolving disc 36 is a scale 4| which has markings 40 from 0 degrees- 40 minutes to 50 degrees by decreasing increments on the front side 21 of the base H] of the computer. It is marked at 42 by Latitude difference or equivalent latitude difference. On pivot is also rotatably mounted, over the above discs, and independently movable, a transparent cursor 43, having a center line 44. On base H) on side marked Front 21 are markings 45 Distance and course computer, and at 46 is a conversion scale of statute and nautical miles.

We may now illustrate the operation and use of the instrument.

PROBLEM No. 1

Solve for the rhumb-line distance and course- From: Honolulu. (2125" N. lat., l57-35' W. long.).

To: Santa Ana, Calif, (33-45' N. lat., 117-50' W. long.)

'With all problems, three things must be known in order to operate the computer.

1. Difference of latitude in degrees and minutes (DL).

2. Difference of longitude in degrees and minutes (DLo).

3. Mid-latitude in degrees and minutes (ML).

Problem No. 1 deals with a trip (e. g., by airplane) from Honolulu to Santa Ana, California:

the hair-line 22 of the cursor 2|. is 2,245 nautical miles.

2. Solve for Course on front side 21 of the computer as illustrated in Figure 2. Rotate the cursor 43 to bring the hair-line 44 over the difference of latitude (12-20') on the scale 4|. Then revolve the disc 36 until the distance of 2,245 is directly under the hair-line 44, the latter standing over 12-20' on scale 4|. Read the Course above the arrow 39 of 70% on the scale 30. Since the direction of flight is north and east the True course is 70%".

Figures 1 and 2 of the drawings show the parts in this relation.

PROBLEM No. 2

Solve the rhumb-line distance and course- From: Panama, (8-55' N. lat., '79-30' W. long).

To: St. Louis, Mo., (38-30' N. lat., -15' W. long).

Difference of latitude, 29-35' (DL).

Difference of longitude, 10-45' (DLo).

Mid-latitude, 23-42 (23.7) (ML).

1. Solve for distance in the same manner as in Problem No. 1 by bringing the arrow 41 of the longitude disc opposite 29-35'. Then adjusting mid-latitude reading 23.7", on the cursor 2| over the difference of longitude 1045 reading the distance of 1,869 nautical miles under the hairline of the cursor 2| on the rhumb-line distance scale.

2. In solving for Course in the same manner as in Problem No. 1 by placing the distance of 1,869 over DL (difierence of latitude) of 29-35 we find that the arrow points to warning. Therefore course must be solved by using the Equivalent difierence of latitude.

3. The Equivalent difference of latitude is solved on the back side of the computer. Place the arrow of the difference of longitude disc over zero. Place the slide of the mid-latitude scale at midlatitude of 2342 A Revolve cursor 2| until the mid-latitude of 23-42%;' is directly over the difference of longitude of 1045. Read the Equivalent difference of latitude of 945 beneath the cross-hair 26, on the slide.

4. Solve for Course on the front 21. Rotate the cursor 43 to bring the cross-hair 44 over the equivalent difierence of latitude of 9-45'. Revolve the distance disc 36, and read 1,869 directly under the cross-hair while the latter is'still over 945. Read Course of 18 A above arrow on the inner scale of 45 to 0-30' clockwise. Since the flight is north and west the True Course is found by subtracting 18/i from 360 and is 341%.

Due to fineness of graduation on rule. short courses are difficult to read when the given latitude and longitude differences are used. For accurate solution, multiply the longitude and latitude differences (not mid-latitude) by some convenient factor and divide the answer by the factor.

This distance Using DLo30-0-and proceeding as in Problem N0. 1 we get a distance reading of 1,727 nautical miles. This, divided by factor 10 gives us 172.7 nautical miles. For course, place 172.7 over 1-30' and read a course of 58 /2.

To determine the Equivalent DL where the DLo is extremely small, such as -7: Using a factor of 10 gives 70' or 1-l0 which is under and still is not easily read. Therefore in this example a factor of 100 is suggested giving 700' or 11-40'. Now assuming a ML of 30 we read an equivalent DL of -20' (620) and dividing by 100 gives 0-6.2', the true Equivalent DL. Now multiply both the true distance and. the Equivalent DL by 10 in this example which give an Equivalent DL of 62' or 1-2' and solve for course which will be between 045.

LEGENDS The legend shows the course angle obtained by the instrument. Thus:

If flying in the southwesterly quadrant, the azimuth is obtained by adding 180 to the reading of the computer.

If flying in the northwesterly quadrant, the azimuth is obtained by subtracting the reading from 360.

If flying in the southeasterly quadrant, the azimuth is obtained by subtracting the reading from 180.

If flying in the northeasterly quadrant, the computer reading is the azimuth.

To explain the use of distance scale l4 reading from zero to 3,000 nautical miles and from 3,000 to 4,243 nautical miles: The setting of the midlatitude cursor 2| is always assumed to start at zero miles to be swung in clock-wise direction until an intersection is had with the difierence of longitude reading and mid-latitude reading. When this intersection is had within the first revolution or 360', the reading is between zero and 3,000 nautical miles. When an intersection of the midlatitude and mid-longitude scales is had on the second revolution or between 360 and 720, the

reading is somewhere between 3,000 and 4,243 nautical miles.

In the above description cursors 2| and 43 are describedas transparent and carryinglines 22 and 44 which extend from the center of the pivot -I I. But it will be understood that the cursors could be opaque, one edge of the cursor being in line with the center of pivot H. We do not wish to restrict invention to transparent cursors.

What is claimed as new is:

1. A navigational instrument comprising a flat base member provided with a center pivot, a revolvable disc on said pivot, said disc having thereon a series of spirals indicating longitude distances, a rotary cursor on said pivot and having a scale of graduations indicating mid-latitude, a second scale having divisions indicating latitude diiferences or equivalent latitude differences on said base member and surrounding the periphery of said disc, and a third scale having divisions indicating rhumb-line distances in nautical miles on said base member outside of and surrounding said second scale.

2. A navigation instrument comprising a fiat base, a pivot thereon, a disc revolvable on said pivot, said base carrying a scale surrounding the periphery of said disc and indicating latitude difierence or equivalent latitude difference, said base also having a second scale surrounding the first mentioned one and indicating rhumb-line distance in nautical miles, said revolvable disc having thereon a series of curves indicating longitude difierences and a pointer to coact with the cursor to coact with said mid-latitude scale and said curves.

JOHN E. CLEMONS. JOHN G. NELSON. 

